Communications in Information and Systems

Volume 10 (2010)

Number 4

Kinematics of the Rolling Sphere and Quantum Spin

Pages: 221 – 238



Anthony M. Bloch

Alberto G. Rojo


We consider the kinematics and control of a sphere rolling of a curved surface and analyze its rotation by mapping the system to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. This mapping is useful in understanding the role of the geometrical phase and generalizes the kinematic control problem of a ball rolling on a plane.

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